Two projects have different payoffs and cost structures with respect to time. When evaluated, they have the following benefits $($B$)$ and costs $($C$)$ in years $0$ through $4.$

$\backslash$table$[[$Year$,$Project A$,$Project B$],[$Benefit$,$Cost,Benpfit.,Cost$],[0,$$$100,50,50,$$$100],[1,$$$100,50,543,50],[2,$$$0,$$$50,$$$43,50],[3,50,550,543,$S$0],[4,50,$$$50,343,$so$],[$Approximate NPV$,60,,60,]]$

$NPV=(B_0-C_0)\frac{B_1-C_1}{1r}\frac{B_2-C_2}{(1r{)}^2}$ dots $\frac{B_a-C_2}{(1r{)}^4}$

$B$ and $C$ are benefits and costs. The subscripts refer to periods $($years$),$ and $r$ is the discount rate, $3\%$ in this case.

a$.$ Which project is to be preferred and why?

b$.$ Would raising the discount rate favor one project over the other? Why?